phd in theoretical physics caltech

Visitors and Visiting Associates

Postdoctoral Scholars

Graduate Students

Research Staff

No results., administrative staff.

Postdoctoral Fellows of the Burke Institute

The Burke Institute has several endowed fellowships for distinguished postdoctoral scholars in theoretical physics such as the Sherman Fairchild Prize Postdoctoral Fellowships, David and Ellen Lee Distinguished Fellowships, and McCone, DuBridge, and Tolman Fellowships. The support offered by these fellowships enables theorists to pursue innovative research.

Over 95 percent of the more than 120 former endowed fellows hold distinguished academic positions. These scholars work on every continent except Antarctica.

For postdoctoral fellowship applications, check here .

In February 2015, some former fellows gathered at Caltech for the Inaugural Celebration and Symposium of the Burke Institute .

Current Fellows of the Burke Institute

2023 - 2026.

2022 - 2025

Past Postdoctoral Fellows

Sherman fairchild prize fellowship, tolman fellowship, mccone fellowship, dubridge fellowship, david and ellen lee fellowship, bantrell fellowship, napf fellowship, weingart fellowship, research assistant professors.

Courses 2023-24

Classical Mechanics and Electromagnetism

The first year of a two-year course in introductory classical and modern physics. Topics: Newtonian mechanics in Ph 1 a; electricity and magnetism, and special relativity, in Ph 1 b, c. Emphasis on physical insight and problem solving. Ph 1 b, c is divided into two tracks: the Practical Track emphasizing practical electricity, and the Analytic Track, which teaches and uses methods of multivariable calculus. Students enrolled in the Practical Track are encouraged to take Ph 8 bc concurrently. Students will be given information helping them to choose a track at the end of fall term.

Waves, Quantum Mechanics, and Statistical Physics

An introduction to several areas of physics including applications in modern science and engineering. Topics include discrete and continuous oscillatory systems, wave mechanics, applications in telecommunications and other areas (first term); foundational quantum concepts, the quantum harmonic oscillator, the Hydrogen atom, applications in optical and semiconductor systems (second term); ensembles and statistical systems, thermodynamic laws, applications in energy technology and other areas (third term). Although best taken in sequence, the three terms can be taken independently.

Introductory Physics Laboratory

Introduction to experimental physics and data analysis, with techniques relevant to all fields that deal in quantitative data. Specific physics topics include ion trapping, harmonic motion, mechanical resonance, and precision interferometry. Broader skills covered include introductions to essential electronic equipment used in modern research labs, basic digital data acquisition and analysis, statistical interpretation of quantitative data, professional record keeping and documentation of experimental research, and an introduction to the Mathematica programming language. Only one term may be taken for credit.

First-Year Seminar: Astrophysics and Cosmology with Open Data

Analog electronics for physicists.

A fast-paced laboratory course covering the design, construction, and testing of practical analog and interface circuits, with emphasis on applications of operational amplifiers. No prior experience with electronics is required. Basic linear and nonlinear elements and circuits are studied, including amplifiers, filters, oscillators and other signal conditioning circuits. Each week includes a 45 minute lecture/recitation and a 2½ hour laboratory. The course culminates in a two-week project of the student's choosing.

Physics Laboratory

A laboratory introduction to experimental physics and data analysis. Experiments use research-grade equipment and techniques to investigate topics in classical electrodynamics, resonance phenomena, waves, and other physical phenomena. Students develop critical, quantitative evaluations of the relevant physical theories; they work individually and choose which experiments to conduct. Each week includes a 30-minute individual recitation and a 3 hour laboratory.

A laboratory course continuing the study of experimental physics introduced in Physics 6. The course introduces some of the equipment and techniques used in quantum, condensed matter, nuclear, and particle physics. The menu of experiments includes some classics which informed the development of the modern quantum theory, including electron diffraction, the Stern-Gerlach experiment, Compton scattering, and the Mössbauer Effect. The course format follows that of Physics 6: students work individually and choose which experiments to conduct, and each week includes a 30 minute individual recitation and a 3 hour laboratory.

Experiments in Electromagnetism

A two-term sequence of experiments that parallel the material of Ph 1 bc. It includes measuring the force between wires with a homemade analytical balance, measuring properties of a 1,000-volt spark, and building and studying a radio-wave transmitter and receiver. The take-home experiments are constructed from a kit of tools and electronic parts. Measurements are compared to theoretical expectations.

First-Year Seminar: The Science of Music

This course will focus on the physics of sound, how musical instruments make it, and how we hear it, including readings, discussions, demonstrations, and student observations using sound analysis software. In parallel we will consider what differentiates music from other sounds, and its role psychically and culturally. Students will do a final project of their choice and design, with possibilities including analysis of recordings of actual musical instruments, instrument construction and analysis, and tests or surveys of people's abilities or preferences. First-year (undergraduate) only; limited enrollment.

Frontiers in Physics

Open for credit to first-year students and sophomores. Weekly seminar by a member of the physics department or a visitor, to discuss their research at an introductory level; the other class meetings will be used to explore background material related to seminar topics and to answer questions that arise. The course will also help students find faculty sponsors for individual research projects. Graded pass/fail.

First-Year Seminar: Beyond Physics

First-year students are offered the opportunity to enroll in this class by submitting potential solutions to problems posed in the fall term. A small number of solutions will be selected as winners, granting those students permission to register. This course demonstrates how research ideas arise, are evaluated, and tested and how the ideas that survive are developed. Weekly group discussions and one-on-one meetings with faculty allow students to delve into cutting edge scientific research. Ideas from physics are used to think about a huge swath of problems ranging from how to detect life on extrasolar planets to exploring the scientific underpinnings of science fiction in Hollywood films to considering the efficiency of molecular machines. Support for summer research at Caltech between an undergraduate's first and sophomore years will be automatic for students making satisfactory progress. Graded pass/fail. First-year (undergraduates) only; limited enrollment.

Waves, Quantum Physics, and Statistical Mechanics

A one-year course primarily for students intending further work in the physics option. Topics include classical waves; wave mechanics, interpretation of the quantum wave-function, one-dimensional bound states, scattering, and tunneling; thermodynamics, introductory kinetic theory, and quantum statistics.

Computational Physics Laboratory I

Introduction to the tools of scientific computing. Use of numerical algorithms and symbolic manipulation packages for solution of physical problems. Python for scientific programming, Mathematica for symbolic manipulation, Unix tools for software development. Offered first and second terms.

Computational Physics Laboratory II

Computational tools for data analysis. Use of python for accessing scientific data from the web. Bayesian techniques. Fourier techniques. Image manipulation with python. Offered second and third terms.

Computational Physics Laboratory III

Computational tools and numerical techniques. Applications to problems in classical mechanics. Numerical solution of 3-body and N-body systems. Monte Carlo integration. Offered third term only.

Caltech Physics League

This course serves as a physics club, meeting weekly to discuss and analyze real-world problems in physical sciences. A broad range of topics will be considered, such as energy production, space and atmospheric phenomena, astrophysics, nano-science, and others. Students will use basic physics knowledge to produce simplified (and perhaps speculative) models of complex natural phenomena. In addition to regular assignments, students will also compete in solving challenge problems each quarter with prizes given in recognition of the best solutions.

Oral and Written Communication

Provides practice and guidance in oral and written communication of material related to contemporary physics research. Students will choose a topic of interest, make presentations of this material in a variety of formats, and, through a guided process, draft and revise a technical or review article on the topic. The course is intended for senior physics majors. Fulfills the Institute scientific writing requirement.

Advanced Physics Laboratory

Advanced preparation for laboratory research. Dual emphasis on practical skills used in modern research groups and historic experiments that illuminate important theoretical concepts. Topics include advanced signal acquisition, conditioning, and data processing, introductions to widely-used optical devices and techniques, laser-frequency stabilization, and classic experiments such as magnetic resonance, optical pumping, and doppler-free spectroscopy. Fundamentals of vacuum engineering, thin-film sample growth, and cryogenics are occasionally offered. Special topics and student-led projects are available on request.

Senior Thesis (Experiment)

Senior thesis (theory).

Open only to senior physics majors. Theoretical research must be supervised by a faculty member, the student's thesis adviser. Two 15-minute presentations to the Physics Undergraduate Committee are required, one near the end of the first term and one near the end of third term. The written thesis must be completed and distributed to the committee one week before the second presentation. Students wishing assistance in finding an adviser and/or a topic for a senior thesis are invited to consult with the chair of the Physics Undergraduate Committee, or any other member of this committee. A grade will not be assigned in Ph 79 until the end of the third term. P grades will be given the first two terms, and then changed at the end of the course to the appropriate letter grade. Not offered on a pass/fail basis.

Order-of-Magnitude Physics

Emphasis will be on using basic physics to understand complicated systems. Examples will be selected from properties of materials, geophysics, weather, planetary science, astrophysics, cosmology, biomechanics, etc. Given in alternate years. Not offered 2023-24.

Relativistic Astrophysics

This course is designed primarily for junior and senior undergraduates in astrophysics and physics. It covers the physics of black holes and neutron stars, including accretion, particle acceleration and gravitational waves, as well as their observable consequences: (neutron stars) pulsars, magnetars, X-ray binaries, gamma-ray bursts; (black holes) X-ray transients, tidal disruption and quasars/active galaxies and sources of gravitational waves.

A laboratory course intended for graduate students, it covers the design, construction, and testing of simple, practical analog and interface circuits useful for signal conditioning and experiment control in the laboratory. No prior experience with electronics is required. Students will use operational amplifiers, analog multipliers, diodes, bipolar transistors, and passive circuit elements. Each week includes a 45 minute lecture/recitation and a 2½ hour laboratory. The course culminates in a two-week project of the student's choosing.

Topics in Classical Physics

An intermediate course in the application of basic principles of classical physics to a wide variety of subjects. Ph 106 a will be devoted to mechanics, including Lagrangian and Hamiltonian formulations of mechanics, small oscillations and normal modes, central forces, and rigid-body motion. Ph 106 b will be devoted to fundamentals of electrostatics, magnetostatics, and electrodynamics, including boundary-value problems, multipole expansions, electromagnetic waves, and radiation. It will also cover special relativity. Ph 106 c will cover advanced topics in electromagnetism and an introduction to classical optics.

Classical and Laser Optics

Noise and stochastic resonance.

The presence of noise in experimental systems is often regarded as a nuisance since it diminishes the signal to noise ratio thereby obfuscating weak signals or patterns. From a theoretical perspective, noise is also problematic since its influence cannot be elicited from deterministic equations but requires stochastic-based modeling which incorporates various types of noise and correlation functions. In general, extraction of embedded information requires that a threshold be overcome in order to outweigh concealment by noise. However, even below threshold, it has been demonstrated in numerous systems that external forcing coupled with noise can actually boost very weak signatures beyond threshold by a phenomenon known as stochastic resonance. Although it was originally demonstrated in nonlinear systems, more recent studies have revealed this phenomenon can occur in linear systems subject, for example, to color-based noise. Techniques for optimizing stochastic resonance are now revolutionizing modeling and measurement theory in many fields ranging from nonlinear optics and electrical systems to condensed matter physics, neurophysiology, hydrodynamics, climate research and even finance. This course will be conducted in survey and seminar style and is expected to appeal to theorists and experimentalists alike. Review of the current literature will be complimented by background readings and lectures on statistical physics and stochastic processes as needed. Part b not offered 2023-24.

Physics of Measurement

Physics of measurement: moonbounce and beyond - microwave scattering for communications and metrology, quantum cryptography.

This course is an introduction to quantum cryptography: how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically. The course covers the fundamental ideas of quantum information that form the basis for quantum cryptography, such as entanglement and quantifying quantum knowledge. We will introduce the security definition for quantum key distribution and see protocols and proofs of security for this task. We will also discuss the basics of device-independent quantum cryptography as well as other cryptographic tasks and protocols, such as bit commitment or position-based cryptography. Not offered 2023-24.

Computational Physics Lab

Many of the recent advances in physics are attributed to progress in computational power. In the advanced computational lab, students will hone their computational skills by working through projects inspired by junior level classes (such as classical mechanics and E, statistical mechanics, quantum mechanics and quantum many-body physics). This course will primarily be in Python and Mathematica. This course is offered pass/fail. Part a and part b not offered 2023-24.

Quantum Mechanics

A one-year course in quantum mechanics and its applications, for students who have completed Ph 12 or Ph 2. Wave mechanics in 3-D, scattering theory, Hilbert spaces, matrix mechanics, angular momentum, symmetries, spin-1/2 systems, approximation methods, identical particles, and selected topics in atomic, solid-state, nuclear, and particle physics.

Statistical Physics of Interacting Systems, Phases, and Phase Transitions

An advanced course in statistical physics that focuses on systems of interacting particles. Part a will cover interacting gases and spin models of magnetism, phase transitions and broken symmetries, classical field theories, and renormalization group approach to collective phenomena. Part b will introduce the path-integral based quantum to classical statistical mechanics mapping, as well as dualities and topological-defects descriptions, with applications to magnets, superfluids, and gauge field theories.

Mathematical Methods of Physics

Mathematical methods and their application in physics. First term focuses on group theoretic methods in physics. Second term includes analytic methods such as complex analysis, differential equations, integral equations and transforms, and other applications of real analysis. Third term covers probability and statistics in physics. Each part may be taken independently. Part c not offered 2023-24.

Introduction to Condensed Matter

This course is an introduction to condensed matter which covers electronic properties of solids, including band structures, and transport. In addition, the course will introduce topological band-structure effects, covering Berry phase, the Thouless pump, and topological insulators. Ph 135 is continued by Ph/APh 223 ab in the winter and spring terms.

Applications of Classical Physics

Applications of classical physics to topics of interest in contemporary "macroscopic" physics. Continuum physics and classical field theory; elasticity and hydrodynamics; plasma physics; magnetohydrodynamics; thermodynamics and statistical mechanics; gravitation theory, including general relativity and cosmology; modern optics. Content will vary from year to year, depending on the instructor. An attempt will be made to organize the material so that the terms may be taken independently. Ph 136 a will focus on thermodynamics, statistical mechanics, random processes, and optics. Ph 136 b will focus on fluid dynamics, MHD, turbulence, and plasma physics. Ph 136 c will cover an introduction to general relativity. Given in alternate years. Not offered 2023-24.

Atoms and Photons

Quantum hardware and techniques.

This class covers multiple quantum technology platforms and related theoretical techniques, and will provide students with broad knowledge in quantum science and engineering. It will be split into modules covering various topics including solid state quantum bits, topological quantum matter, trapped atoms and ions, applications of near-term quantum computers, superconducting qubits. Topics will alternate from year to year.

Introduction to Elementary Particle Physics

This course provides an introduction to particle physics which includes Standard Model, Feynman diagrams, matrix elements, electroweak theory, QCD, gauge theories, the Higgs mechanism, neutrino mixing, astro-particle physics/cosmology, accelerators, experimental techniques, important historical and recent results, physics beyond the Standard Model, and major open questions in the field.

Fundamentals of Fluid Flow in Small Scale Systems

Research efforts in many areas of applied science and engineering are increasingly focused on microsystems involving active or passive fluid flow confined to 1D, 2D or 3D platforms. Intrinsically large ratios of surface to volume can incur unusual surface forces and boundary effects essential to operation of microdevices for applications such as optofluidics, bioengineering, green energy harvesting and nanofilm lithography. This course offers a concise treatment of the fundamentals of fluidic behavior in small scale systems. Examples will be drawn from pulsatile, oscillatory and capillary flows, active and passive spreading of liquid dots and films, thermocapillary and electrowetting systems, and instabilities leading to self-sustaining patterns. Students must have working knowledge of vector calculus, ODEs, basic PDEs, and complex variables. Not offered 2023-24.

Fundamentals of Energy and Mass Transport in Small Scale Systems

Reading and independent study, research in physics, advanced experimental physics.

A one-term laboratory course which will require students to design, assemble, calibrate, and use an apparatus to conduct a nontrivial experiment involving quantum optics or other current research area of physics. Students will work as part of a small team to reproduce the results of a published research paper. Each team will be guided by an instructor who will meet weekly with the students; the students are each expected to spend an average of 4 hours/week in the laboratory and the remainder for study and design. Enrollment is limited. Permission of the instructors required.

Neural Computation

This course aims at a quantitative understanding of how the nervous system computes. The goal is to link phenomena across scales from membrane proteins to cells, circuits, brain systems, and behavior. We will learn how to formulate these connections in terms of mathematical models, how to test these models experimentally, and how to interpret experimental data quantitatively. The concepts will be developed with motivation from some of the fascinating phenomena of animal behavior, such as: aerobatic control of insect flight, precise localization of sounds, sensing of single photons, reliable navigation and homing, rapid decision-making during escape, one-shot learning, and large-capacity recognition memory. Not offered 2023-2024.

Special Topics in Physics

Topics will vary year to year and may include hands-on laboratory work, team projects and a survey of modern physics research.

Candidacy Physics Fitness

The course will review problem solving techniques and physics applications from the undergraduate physics college curriculum. In particular, we will touch on the main topics covered in the written candidacy exam: classical mechanics, electromagnetism, statistical mechanics and quantum physics, optics, basic mathematical methods of physics, and the physical origin of everyday phenomena.

Nuclear Physics

An introduction and overview of modern topics in nuclear physics, including models and structure of nucleons, nuclei and nuclear matter, the electroweak interaction of nuclei, and nuclear/neutrino astrophysics.

Relativistic Quantum Field Theory

Quantum computation.

The theory of quantum information and quantum computation. Overview of classical information theory, compression of quantum information, transmission of quantum information through noisy channels, quantum error-correcting codes, quantum cryptography and teleportation. Overview of classical complexity theory, quantum complexity, efficient quantum algorithms, fault-tolerant quantum computation, physical implementations of quantum computation.

Advanced Condensed-Matter Physics

Advanced mathematical methods of physics.

Advanced topics in geometry and topology that are widely used in modern theoretical physics. Emphasis will be on understanding and applications more than on rigor and proofs. First term will cover basic concepts in topology and manifold theory. Second term will include Riemannian geometry, fiber bundles, characteristic classes, and index theorems. Third term will include anomalies in gauge-field theories and the theory of Riemann surfaces, with emphasis on applications to string theory. Part c not offered 2023-24.

Elementary Particle Theory

First term: Standard model, including electroweak and strong interactions, symmetries and symmetry breaking (including the Higgs mechanism), parton model and quark confinement, anomalies. Second and third terms: more on nonperturbative phenomena, including chiral symmetry breaking, instantons, the 1/N expansion, lattice gauge theories, and topological solitons. Other topics include topological field theory, precision electroweak, flavor physics, conformal field theory and the AdS/CFT correspondence, supersymmetry, Grand Unified Theories, and Physics Beyond the Standard Model. Part c not offered 2023-24.

Introduction to Topological Field Theory

Topological field theories are the simplest examples of quantum field theories which, in a sense, are exactly solvable and generally covariant. During the past twenty years they have been the main source of interaction between physics and mathematics. Thus, ideas from gauge theory led to the discovery of new topological invariants for 3-manifolds and 4-manifolds. By now, topological quantum field theory (TQFT) has evolved into a vast subject, and the main goal of this course is to give an accessible introduction to this elegant subject. Not offered 2023-24.

Theoretical Cosmology and Astroparticle Physics

Cosmology in an expanding universe, inflation, big bang nucleosynthesis, baryogenesis, neutrino and nuclear astrophysics. Second term: Cosmological perturbation theory and the cosmic microwave background, structure formation, theories of dark matter.

General Relativity

A systematic exposition of Einstein's general theory of relativity and its applications to gravitational waves, black holes, relativistic stars, causal structure of space-time, cosmology and brane worlds. Given in alternate years. Part c not offered 2023-24.

Gravitational Radiation

Special topics in Gravitational-wave Detection. Physics of interferometers, limits of measurement, coherent quantum feedback, noise, data analysis.

Physics Seminar

An introduction to independent research, including training in relevant professional skills and discussion of current Caltech research areas with Caltech faculty, postdocs, and students. One meeting per week plus student projects. Registration restricted to first-year graduate students in physics.

Introduction to String Theory

Thesis research.

Ph 300 is elected in place of Ph 172 when the student has progressed to the point where research leads directly toward the thesis for the degree of Doctor of Philosophy. Approval of the student's research supervisor and department adviser or registration representative must be obtained before registering. Graded pass/fail.

Opportunities for Postdoctoral Scholars

Postodoctoral fellowship opportunities in QSE include:

Caltech hosts a variety of Postdoctoral Scholar positions in each Division. Learn more about current postings by visiting

CCE Postdoctoral Positions Available

EAS Positions Available

PMA Postdoctoral Positions Available

These positions may also be co-listed at applications.caltech.edu .

Positions may also be listed by research groups. Find a list of QSE faculty, along with information about their research area, their Academic Division, and links to their websites, on the QSE Faculty page .

At the Edge of Physics

When new assistant professor of physics Lee McCuller was young, he liked to build things. His uncle made him a power supply, which he integrated with electronic hobby kits from RadioShack to do simple things like use analog circuits to switch lights and motors on and off. Today, McCuller tinkers with what some would call the most advanced measurement device in the world: LIGO , or the Laser Interferometer Gravitational-wave Observatory.

McCuller is an expert on quantum squeezing, a method used at LIGO to make incredibly precise measurements of gravitational waves that travel millions and billions of light-years across space to reach us. When black holes and collapsed stars, called neutron stars, collide, they generate ripples in space-time, or gravitational waves. LIGO's detectors—located in Washington and Louisiana—specialize in picking up these waves but are limited by quantum noise, an inherent property of quantum mechanics that results in photons popping in and out of existence in empty space. Quantum squeezing is a complex method for reducing this unwanted noise.

Research into quantum squeezing and related measurements ramped up as far back as the 1980s, with key theorical studies by Caltech's Kip Thorne (BS '62), Richard P. Feynman Professor of Theoretical Physics, Emeritus, along with physicist Carl Caves (PhD '79) and others worldwide. Those theories inspired the first experimental demonstration of squeezing in 1986 by Jeff Kimble , the William L. Valentine Professor of Physics, Emeritus. The next decades saw many other advances in squeezing research, and now McCuller is at the leading edge of this innovative field. For example, he has been busy developing "frequency-dependent" squeezing that will greatly enhance LIGO's sensitivity when it turns back on in May of this year.

After earning his bachelor's degree from the University of Texas at Austin in 2010, McCuller attended the University of Chicago, where he earned his PhD in physics in 2015. There he began work on an experiment called the Fermilab Holometer, which looked for a speculative type of noise that would link gravity with quantum mechanics. It was during this project that McCuller met LIGO scientists, including MIT's Rai Weiss—who together with Thorne and Barry Barish , the Ronald and Maxine Linde Professor of Physics, Emeritus, won the Nobel Prize in Physics in 2017 for their groundbreaking work on LIGO. McCuller was inspired by Weiss and the LIGO project and decided to join MIT in 2016. He became an assistant professor at Caltech in 2022.

In the future, McCuller hopes to take the quantum measurement tools he has developed for LIGO and apply them to other problems. "If LIGO is the most precise ruler in the world, then we want to make those rulers available to everyone," he says.

We met with McCuller over Zoom to learn more about quantum squeezing and its future applications to other fields as well as what inspired McCuller to join Caltech.

When did you first start working on LIGO?

After I graduated from University of Chicago in 2015, I went to work on LIGO at MIT. When I walked in the door, they were having a meeting about the first detection of gravitational waves! The public didn't know yet, but there had been rumors. It was exciting to learn the rumors were true, and it was nice to see everyone overjoyed that things were working.

There was a local experiment taking place at that time on using squeezed light in the frequency-dependent manner that will start up at LIGO later this year. My job was to help build the first full-scale demonstration of this. The group, before me, had previously demonstrated the concept but not at the full scale. I was there was to show exactly what would be needed to employ it in the LIGO observatories. This required a particularly challenging experimental setup.

Can you attempt to explain what quantum squeezing is?

At each of the observatory locations, LIGO uses laser beams to measure disturbances in space-time—the gravitational waves. The laser beams are shot out at 90-degrees from each other and travel down two 4-kilometer-long arms. They reflect off mirrors and travel back down the arms to meet back up. If a gravitational wave passes through space, it will stretch and squeeze LIGO arms such that the lasers will be pushed out of sync; when they meet back up, the combined laser will create an interference pattern.

At the quantum level, there are photons in the laser light that hit the mirrors at different times. We call this shot noise, or quantum noise. Imagine dumping out a can full of BBs. They all hit the ground and click and clack independently. The BBs are randomly hitting the ground, and that creates a noise. The photons are like the BBs and hit LIGO's mirrors at irregular times. Quantum squeezing, in essence, makes the photons arrive more regularly as if the photons are holding hands rather than traveling independently. And this means that you can more precisely measure the phase or frequency of the light inside LIGO—and ultimately detect even fainter gravitational waves.

To squeeze light, we are basically pushing the uncertainty inherent in light waves from one feature to another. We are making the light more certain in its phase, or frequency, and less certain in its amplitude, or power [the uncertainty principle says that both the exact frequency and amplitude of a light wave cannot be known at the same time]. To really explain the details of how squeezing actually works is very hard! I primarily know how to use math to describe it.

Can you explain more about how the quantum squeezing technology works at LIGO?

An interesting thing about squeezed light is that we aren't doing anything to the actual laser. We don't even touch it. When we operate LIGO, we offset the arms so that its wave interference is not perfectly dark—a small amount of light gets through. The little bit of light that remains has an electrical field that interferes with quantum fluctuations in the vacuum, or empty space, and this leads to the shot noise or the photons acting like BBs as we talked about earlier. When we squeeze light, we are actually squeezing the vacuum so that the photons have lower uncertainty in their frequency.

What does the new "frequency-dependent" technique you are working on entail?

Up until now, we have been squeezing light in LIGO to reduce uncertainty in the frequency. This allows us to be more sensitive to the high-frequency gravitational waves within LIGO's range. But if we want to detect lower frequencies—which occur earlier in, say, a black hole merger, before the bodies collide—we need to do the opposite: we want to make the light's amplitude, or power, more certain and the frequency less certain. At the lower frequencies, the shot noise, our BB-like photons, push the mirrors around in different ways. We want to reduce that. Our new frequency-dependent cavity at the LIGO detectors is designed to reduce the frequency uncertainty in the high frequencies and the amplitude uncertainties in the low frequencies. The goal is to win everywhere and reduce the unwanted mirror motions.

Part of the reason this technology is more important in the next run is because we are turning up the power on our lasers. With more power, you get more pressure on the mirrors. Our new squeezing technology will allow us to turn the power up without creating the unwanted mirror motions.

What this means is that we will be even more sensitive to the early phases of black hole and neutron star mergers, and that we can see even fainter mergers.

What other projects are you working on?

One project I'm working on involves Kathryn Zurek and Rana Adhikari. We are building a tabletop-size detector that will attempt to pick up signatures of quantum gravity , or pixels in space and time as some people say. The idea there is to make interferometers more like high-energy-physics detectors. The detectors would click when something passes through it, largely circumventing the impacts of shot noise. I love the motivation of the project—quantum gravity, which is the quest to merge theories of gravity with quantum physics. It is a very lofty goal.

In general, what I hope to do is grow from the LIGO work and apply quantum measurement techniques to not only enhance the gravitational wave detectors but also to see where other fundamental physics experiments or technologies can be improved. I want to use quantum optics not necessarily for computation or for information but for measurement. Squeezing light is one of the first demonstrations of these concepts in a real experiment. The hope is that we can keep using these quantum techniques in more and more experiments. We want to take the advantages of LIGO and find all the places where we can apply them.

What made you chose Caltech?

Caltech has a lot of mission-oriented scientists. It's not just about learning or demonstrating or exploring—it's the mix of all these things. I like a place where the goal is to integrate technologies and do new experiments. Take LIGO for instance. Few people know how the whole thing works and many of them are here. Caltech is a place where people understand that what we are doing is hard. Good projects require both narrow and broad expertise, and a combination of the right people. The students are similarly motivated by both the science goals and the process. We are not just trying to build something that reliably works, we are also trying to build something that's at the edge of what is possible.

Watson Lecture: Zhongwen Zhan (PhD '13) Discusses His Odyssey to the South Pole

What can Antarctica tell us about global sea level rise? On Wednesday, April 24, 2024, at 7:30 p.m. PT in Caltech's Beckman Auditorium, Zhognwen Zhan , professor of geophysics and a member of Caltech's Seismological Laboratory, will explain how understanding the behavior of the Antarctic ice sheet at its base is crucial to forecasting future ocean levels.

In a public talk called "Voices of the Ice: A Seismic Odyssey to the South Pole" that continues the 101st season of the Watson Lectures, Zhan will describe a monthlong research expedition he took to Antarctica in December 2022 to explore an innovative method for detecting seismic waves in ice. By using telecommunication lines buried in ice to pick up vibrations, he aims to learn more about the physics and deep structure of glaciers and ice sheets, and how the polar regions are changing amid ongoing climate change. In this talk, Zhan will also share some of the personal experiences of the journey that reshaped his perspective, not just on geophysics but on life as a scientist.

"The South Pole trip certainly was a transformative one," Zhan says. "You suddenly switch from a busy environment to a vast wide continent that's so empty. The only thing you can focus on is your experiment, your research. It's interesting to see how scientists work in an exotic place, learning about critical processes that are important to our Earth, to human society."

Starting at 6 p.m. outside Beckman Auditorium, representatives of the Seismo Lab will be available to answer questions about seismologic advances and their applications around the world.

Originally from China, Zhan earned a PhD in geophysics from Caltech in 2013. Prior to joining the faculty at Caltech in 2015, he was a postdoctoral researcher at UC San Diego. Zhan's research focus is on two geophysical topics, ambient seismic noise and subduction zone processes. He and his lab use fiber-optic sensing technologies to build next-generation seismic networks, both on land and in the ocean, which also have applications in areas outside conventional geophysics, such as global ocean warming, groundwater monitoring, and cryoseismology.

The Watson Lectures offer new opportunities each month to hear how Caltech's premier researchers are tackling society's most pressing challenges and inventing the technologies of the future. Join friends and neighbors outside Beckman Auditorium to enjoy food, drinks, and music together before each lecture. Interactive displays related to the evening's topic will give audience members additional context and information. The festivities start at 6 p.m. Guests are also encouraged to stay for post-talk coffee and tea as well as the chance to converse with attendees and researchers.

Learn more about the Earnest C. Watson Lecture Series and its history at Caltech.edu/Watson.

Watson Lectures are free and open to the public. Register online . A recording will be made available after the live event.

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April 10, 2024

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Physicists discover a novel quantum state in an elemental solid

by Princeton University

Physicists have observed a novel quantum effect termed "hybrid topology" in a crystalline material. This finding opens up a new range of possibilities for the development of efficient materials and technologies for next-generation quantum science and engineering.

The finding, published in Nature , came when Princeton scientists discovered that an elemental solid crystal made of arsenic (As) atoms hosts a never-before-observed form of topological quantum behavior. They were able to explore and image this novel quantum state using a scanning tunneling microscope (STM) and photoemission spectroscopy, the latter a technique used to determine the relative energy of electrons in molecules and atoms.

This state combines, or "hybridizes," two forms of topological quantum behavior—edge states and surface states, which are two types of quantum two-dimensional electron systems. These have been observed in previous experiments, but never simultaneously in the same material where they mix to form a new state of matter.

"This finding was completely unexpected," said M. Zahid Hasan, the Eugene Higgins Professor of Physics at Princeton University, who led the research. "Nobody predicted it in theory before its observation."

In recent years, the study of topological states of matter has attracted considerable attention among physicists and engineers and is presently the focus of much international interest and research. This area of study combines quantum physics with topology—a branch of theoretical mathematics that explores geometric properties that can be deformed but not intrinsically changed.

For more than a decade, scientists have used bismuth (Bi)-based topological insulators to demonstrate and explore exotic quantum effects in bulk solids mostly by manufacturing compound materials, like mixing Bi with selenium (Se), for example. However, this experiment is the first time topological effects have been discovered in crystals made of the element As.

"The search and discovery of novel topological properties of matter have emerged as one of the most sought-after treasures in modern physics, both from a fundamental physics point of view and for finding potential applications in next-generation quantum science and engineering," said Hasan. "The discovery of this new topological state made in an elemental solid was enabled by multiple innovative experimental advances and instrumentations in our lab at Princeton."

An elemental solid serves as an invaluable experimental platform for testing various concepts of topology. Up until now, bismuth has been the only element that hosts a rich tapestry of topology, leading to two decades of intensive research activities. This is partly attributed to the material's cleanliness and the ease of synthesis. However, the current discovery of even richer topological phenomena in arsenic will potentially pave the way for new and sustained research directions.

"For the first time, we demonstrate that akin to different correlated phenomena, distinct topological orders can also interact and give rise to new and intriguing quantum phenomena," Hasan said.

A topological material is the main component used to investigate the mysteries of quantum topology. This device acts as an insulator in its interior, which means that the electrons inside are not free to move around and, therefore, do not conduct electricity.

However, the electrons on the device's edges are free to move around, meaning they are conductive. Moreover, because of the special properties of topology, the electrons flowing along the edges are not hampered by any defects or deformations. This type of device has the potential not only to improve technology but also to generate a greater understanding of matter itself by probing quantum electronic properties.

Hasan noted that there is much interest in using topological materials for practical applications. But two important advances need to happen before this can be realized. First, quantum topological effects must be manifested at higher temperatures. Second, simple and elemental material systems (like silicon for conventional electronics) that can host topological phenomena need to be found.

"In our labs, we have efforts in both directions—we are searching for simpler materials systems with ease of fabrication where essential topological effects can be found," said Hasan. "We are also searching for how these effects can be made to survive at room temperature."

Background of the experiment

The discovery's roots lie in the workings of the quantum Hall effect—a form of topological effect that was the subject of the Nobel Prize in Physics in 1985. Since that time, topological phases have been studied, and many new classes of quantum materials with topological electronic structures have been found. Most notably, Daniel Tsui, the Arthur Legrand Doty Professor of Electrical Engineering, Emeritus, at Princeton, won the 1998 Nobel Prize in Physics for discovering the fractional quantum Hall effect.

Similarly, F. Duncan Haldane, the Eugene Higgins Professor of Physics at Princeton, won the 2016 Nobel Prize in Physics for theoretical discoveries of topological phase transitions and a type of two-dimensional (2D) topological insulator. Subsequent theoretical developments showed that topological insulators can take the form of two copies of Haldane's model based on the electron's spin-orbit interaction.

Hasan and his research team have been following in the footsteps of these researchers by investigating other aspects of topological insulators and searching for novel states of matter. This led them, in 2007, to the discovery of the first examples of three-dimensional (3D) topological insulators. Since then, Hasan and his team have been on a decade-long search for a new topological state in its simplest form that can also operate at room temperature.

"A suitable atomic chemistry and structure design coupled to first-principles theory is the crucial step to make topological insulator's speculative prediction realistic in a high-temperature setting," said Hasan.

"There are hundreds of quantum materials, and we need both intuition, experience, materials-specific calculations and intense experimental efforts to find the right material for in-depth exploration eventually. And that took us on a decade-long journey of investigating many bismuth-based materials, leading to many foundational discoveries."

The experiment

Bismuth-based materials are capable, at least in principle, of hosting a topological state of matter at high temperatures. However, these require complex materials preparation under ultra-high vacuum conditions, so the researchers decided to explore several other systems. Postdoctoral researcher Md. Shafayat Hossain suggested a crystal made of arsenic because it can be grown in a form that is cleaner than many bismuth compounds.

When Hossain and Yuxiao Jiang, a graduate student in the Hasan group, turned the STM on the arsenic sample, they were greeted with a dramatic observation—gray arsenic, a form of arsenic with a metallic appearance, harbors both topological surface states and edge states simultaneously.

"We were surprised. Gray arsenic was supposed to have only surface states. But when we examined the atomic step edges, we also found beautiful conducting edge modes," said Hossain.

"An isolated monolayer step edge should not have a gapless edge mode," added Jiang, a co-first author of the study.

This is what is seen in calculations by Frank Schindler, a postdoctoral fellow and condensed matter theorist at the Imperial College London in the United Kingdom, and Rajibul Islam, a postdoctoral researcher at the University of Alabama in Birmingham, Alabama. Both are co-first authors of the paper.

"Once an edge is placed on top of the bulk sample, the surface states hybridize with the gapped states on the edge and form a gapless state," Schindler said.

"This is the first time we have seen such a hybridization," he added.

Physically, such a gapless state on the step edge is not expected for either strong or higher-order topological insulators separately but only for hybrid materials where both kinds of quantum topology are present. This gapless state is also unlike surface or hinge states in strong and higher-order topological insulators , respectively. This meant that the experimental observation by the Princeton team immediately indicated a never-before-observed type of topological state.

David Hsieh, Chair of the Physics Division at Caltech and a researcher who was not involved in the study, pointed to the study's innovative conclusions.

"Typically, we consider the bulk band structure of a material to fall into one of several distinct topological classes, each tied to a specific type of boundary state," Hsieh said. "This work shows that certain materials can simultaneously fall into two classes. Most interestingly, the boundary states emerging from these two topologies can interact and reconstruct into a new quantum state that is more than just a superposition of its parts."

The researchers further substantiated the scanning tunneling microscopy measurements with systematic high-resolution angle-resolved photoemission spectroscopy.

"The gray As sample is very clean, and we found clear signatures of a topological surface state," said Zi-Jia Cheng, a graduate student in the Hasan group and a co-first author of the paper who performed some of the photoemission measurements.

The combination of multiple experimental techniques enabled the researchers to probe the unique bulk-surface-edge correspondence associated with the hybrid topological state—and corroborate the experimental findings.

Implications of the findings

The impact of this discovery is two-fold. The observation of the combined topological edge mode and the surface state paves the way to engineer new topological electron transport channels. This may enable the designing of new quantum information science or quantum computing devices.

The Princeton researchers demonstrated that the topological edge modes are only present along specific geometrical configurations that are compatible with the crystal's symmetries, illuminating a pathway to design various forms of future nanodevices and spin-based electronics.

From a broader perspective, society benefits when new materials and properties are discovered, Hasan said. In quantum materials, the identification of elemental solids as material platforms, such as antimony hosting a strong topology or bismuth hosting a higher-order topology, has led to the development of novel materials that have immensely benefited the field of topological materials.

"We envision that arsenic, with its unique topology, can serve as a new platform at a similar level for developing novel topological materials and quantum devices that are not currently accessible through existing platforms," Hasan said.

The Princeton group has designed and built novel experiments for the exploration of topological insulator materials for over 15 years. Between 2005 and 2007, for example, the team led by Hasan discovered topological order in a three-dimensional bismuth-antimony bulk solid, a semiconducting alloy, and related topological Dirac materials using novel experimental methods.

This led to the discovery of topological magnetic materials. Between 2014 and 2015, they discovered and developed a new class of topological materials called magnetic Weyl semimetals.

The researchers believe this finding will open the door to a whole host of future research possibilities and applications in quantum technologies, especially in so-called "green" technologies.

"Our research is a step forward in demonstrating the potential of topological materials for quantum electronics with energy-saving applications," Hasan said.

Journal information: Nature

Provided by Princeton University

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